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Integrated Tactical and Operational Planning of Police Helicopters
Martijn Mes
Department of Industrial Engineering and Business Information SystemsUniversity of TwenteThe Netherlands
Joint work with: R. van Urk, R. Vromans, K. van Hal, E. Hans, M. Schutten.
Sunday, November 9th, 2014INFORMS Annual Meeting 2014, San Francisco, USA
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INTRODUCTION
To reduce the file size, the original movie (used to give an idea on the activities of the Dutch Aviation Police and Air Support) has been
replaced by this image.
Source: Dutch Aviation Police and Air Support
INFORMS Annual Meeting 2014
INTRODUCTION
Dutch Aviation Police and Air Support Renewed fleet of helicopters with state-of-the-art equipment Planning:
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Decision support
Strategic planning
Tactical planning
Operational scheduling
Nr and type of helicopters, base stations, etc.
Division of flight budget to days, shift times, etc.
When and where to fly on a given day.
Source: Dutch Aviation Police and Air SupportSource: Dutch Aviation Police and Air Support
Source: Dutch Aviation Police and Air Support Source: Dutch Aviation Police and Air Support
INFORMS Annual Meeting 2014
OPERATIONAL SCHEDULING
Decision support system for routing of police helicopters in anticipation of unknown incidents to maximize the weighted expected number of covered
incidents Fixed flight budget Combination of the research fields…
Dynamic and Anticipatory Vehicle Routing Problem Location Covering Problem
We split the problem in (i) forecasting and (ii) routing
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FORECASTING [1/2]
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FORECASTING [2/2]
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Forecast for today, for each time unit (2 minute periods) and each forecast area (hexagonal tiling with hexagons having 2 nautical miles inner radius).
Use all historic incidents to create this forecast for each time and place, but multiply them with a weight depending on Age (more weight on recent observations) Month (high weight if the incident is within the same month
as the forecast day) Weekday (high weight if the incident is on a same weekday
as the forecast day) Space (more weight if the forecast area is close to the area
the incident actually occurred, many weights equal to zero) Time (more weight if the time-of-the-day is close to the time
the incident actually occurred, many weights equal to zero)
ROUTING CHALLENGE
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Being at the right time at the right place
To reduce the file size, the original 3D animation (used to illustrate the idea of being at the right time at the right place) has been replaced by
this image.
ROUTING MODEL
Exact method (MILP) Heuristic procedure:
schedule one helicopter at a time
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APPLICATION
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RESULTS
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Historic data set of incidents for 2 years Use year 1 for learning only Use year 2 to simulate and learn Results:
Normalized such that the number of successful assist of the Dutch Aviation Police & Air Support (in year 2) equals 1
MEDIA
University of Maryland 2013 12/71
HOWEVER…
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Not 9 times as good… Benefits could also have been achieved with relatively
simple policies Effect of dynamic routing small compared to
Setting the departure times Division of flight hours over the year Scheduling shift times Allocation of standby helicopters to various base stations
Tactical planning
TACTICAL PLANNING MODEL
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THE IDEA
Crews10
Flights5
Schiphol (Amsterdam)
Rotterdam
Volkel
43 43
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2 2100
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HOWEVER…
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Only 4% additional improvement Further improvement possible
Impact of standby is relatively large, so why start the heuristic with planning the surveillance flights?
Many options with different types of helicopters at different base stations unexplored
Tactical model difficult to use by the police Unnecessary level of forecast and routing detail in tactical
plan
TACTICAL PLANNING MODEL – NEW FORECAST
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Assumption: relative division of crime independent of time Time: 𝜆 , ,ℎ 𝑑 𝑤=𝛼 ,ℎ 𝑑∗𝛾𝑤 using datasets of last 4 years, with
heavier weight on more recent years Location: kernel density estimation (Silverman, 1986)
Automatically identifyhotspots
Formulate forecast in terms of hotspots (spots with intensity above some threshold)
IMPROVED (?) TACTICAL PLANNING MODEL
Define hourly configurations: Nr of helicopters of each type flying Nr of helicopters of each type on standby The base station of each standby helicopter
Given various restrictions, we have a total of 55 possible configurations
Configurations with flights have predetermined routes Calculate the expected coverage up front for each config. Approach: for each point in time (hours in a year) choose the
best configuration, taking into account several restrictions on sequences of configurations
Final results not yet available…
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CONCLUSIONS
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Operational scheduling Combination of forecasting (generalization in time and
space) and routing (MILP + heuristic) Tactical planning
Simultaneous planning, on an hourly basis for a year in advance, of shifts, flight hours, and standby hours/locations
Both models\applications: Validated with experts and a simulation study Currently used by the Dutch Aviation Police and Air Support
Our research pitfalls Unfair comparison with current practice Too much focus on routing\flights instead of shift planning
QUESTIONS?
Martijn MesAssistant professorUniversity of TwenteSchool of Management and GovernanceDept. Industrial Engineering and Business Information Systems
ContactPhone: +31-534894062Email: [email protected]: http://www.utwente.nl/mb/iebis/staff/Mes/
